Wave front and convex lens

[AdityaDev]

If I have a parallel beam of light parallel to x-axis, with the speed of light varying from bottom to top. Let it decrease from bottom to top. (To get such a beam one can pass the beam through a glass slab normal to its surface, whose refractive index increases linearly from bottom to top). Now although the beam is still parallel to x-axis, the wavefront is tilted. Will a convex lens (principle axis along x) be able to converge the rays at focus? There exists a path difference between two successes ice rays. Hence shouldn't we consider interference? Will there be a bright spot on a screen kept at focal plane but above the focus?

 

[Drakkith]

If I have a parallel beam of light parallel to x-axis, with the speed of light varying from bottom to top. Let it decrease from bottom to top. (To get such a beam one can pass the beam through a glass slab normal to its surface, whose refractive index increases linearly from bottom to top). Now although the beam is still parallel to x-axis, the wavefront is tilted. Will a convex lens (principle axis along x) be able to converge the rays at focus?

If the speed of the wavefront varies, then the beam of light will bend and change direction as it travels, possibly converging or diverging as well. It will no longer be parallel to the X-axis.

 

[AdityaDev]

If the speed of the wavefront varies, then the beam of light will bend and change direction as it travels, possibly converging or diverging as well. It will no longer be parallel to the X-axis.

Actual reason: From huygens principle, direction of velocity is perpendicular to wavefront. Hence direction changes.